<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><title>R: Example data from Gleser, Cronbach and Rajaratnam (1965) to...</title>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<link rel="stylesheet" type="text/css" href="R.css" />
</head><body>

<table width="100%" summary="page for Gleser"><tr><td>Gleser</td><td style="text-align: right;">R Documentation</td></tr></table>

<h2>
Example data from Gleser, Cronbach and Rajaratnam (1965) to show basic principles of generalizability theory. 
</h2>

<h3>Description</h3>

<p>Gleser, Cronbach and Rajaratnam (1965) discuss the estimation of variance components and their ratios as part of their introduction to generalizability theory.  This is a adaptation of their &quot;illustrative data for a completely matched G study&quot; (Table 3).  12 patients are rated on 6 symptoms by two judges.  Components of variance are derived from the ANOVA. 
</p>


<h3>Usage</h3>

<pre>data(Gleser)</pre>


<h3>Format</h3>

<p>A data frame with 12 observations on the following 12 variables. J item by judge:
</p>

<dl>
<dt><code>J11</code></dt><dd><p>a numeric vector</p>
</dd>
<dt><code>J12</code></dt><dd><p>a numeric vector</p>
</dd>
<dt><code>J21</code></dt><dd><p>a numeric vector</p>
</dd>
<dt><code>J22</code></dt><dd><p>a numeric vector</p>
</dd>
<dt><code>J31</code></dt><dd><p>a numeric vector</p>
</dd>
<dt><code>J32</code></dt><dd><p>a numeric vector</p>
</dd>
<dt><code>J41</code></dt><dd><p>a numeric vector</p>
</dd>
<dt><code>J42</code></dt><dd><p>a numeric vector</p>
</dd>
<dt><code>J51</code></dt><dd><p>a numeric vector</p>
</dd>
<dt><code>J52</code></dt><dd><p>a numeric vector</p>
</dd>
<dt><code>J61</code></dt><dd><p>a numeric vector</p>
</dd>
<dt><code>J62</code></dt><dd><p>a numeric vector</p>
</dd>
</dl>



<h3>Details</h3>

<p>Generalizability theory is the application of a components of variance approach to the analysis of reliability.  Given a G study (generalizability) the components are estimated and then may be used in a D study (Decision).  Different ratios are formed as appropriate for the particular D study.
</p>


<h3>Source</h3>

<p>Gleser, G., Cronbach, L., and Rajaratnam, N. (1965). Generalizability of scores influenced by multiple sources of variance. Psychometrika, 30(4):395-418. (Table 3, rearranged to show increasing patient severity and increasing item severity.
</p>


<h3>References</h3>

<p>Gleser, G., Cronbach, L., and Rajaratnam, N. (1965). Generalizability of scores influenced by multiple sources of variance. Psychometrika, 30(4):395-418.
</p>


<h3>Examples</h3>

<pre>
#Find the MS for each component:
#First, stack the data
data(Gleser)
stack.g &lt;- stack(Gleser)
st.gc.df &lt;- data.frame(stack.g,Persons=rep(letters[1:12],12),
Items=rep(letters[1:6],each=24),Judges=rep(letters[1:2],each=12))
#now do the ANOVA
anov &lt;- aov(values ~ (Persons*Judges*Items),data=st.gc.df)
summary(anov)
</pre>


</body></html>
